Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson; Warwick Tucker

doi:10.3934/dcdsb.2009.12.769

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2009, Volume 12, Issue 4: 769-782. Doi: 10.3934/dcdsb.2009.12.769

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Automated computation of robust normal forms of planar analytic vector fields

Tomas Johnson^1, and
Warwick Tucker^2,

1.
Department of Mathematics, Uppsala University, BOX 480, 751 06 Uppsala
2.
Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen

Received: September 30, 2008

Revised: March 31, 2009

Published: October 2009

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Abstract

We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robust in the underlying vector field, and is analytic on a computable neighbourhood of the saddle point. The normal form is suitable for computations aimed at enclosing the flow close to the saddle, and the time it takes a trajectory to pass it. Several examples illustrate the usefulness of this method.

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Mathematics Subject Classification: Primary: 34C20, Secondary: 37M99, 65L70, 65G20.

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